Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain

Abstract

Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The proposed dynamic analysis approach calculated the adjacency matrices from ongoing electroencephalpgram (EEG) in a sliding time-window to form the FCGB sequences. The probability distribution of Shannon entropy was replaced by the connection sequence distribution to measure the uncertainty of FCGB constituting NE. Without averaging, we used time frequency transform of the NE of FCGB sequences to analyze the event-related changes in oscillatory activity in the single-trial traces during the complex cognitive process of driving. Finally, the results of a verification experiment showed that the NE of the FCGB sequences has a certain time-locked performance for different events related to driver fatigue in a prolonged driving task. The time errors between the extracted time of high-power NE and the recorded time of event occurrence were distributed within the range [−30 s, 30 s] and 90.1% of the time errors were distributed within the range [−10 s, 10 s]. The high correlation (r = 0.99997, p < 0.001) between the timing characteristics of the two types of signals indicates that the NE can reflect the actual dynamic interaction states of brain. Thus, the method may have potential implications for cognitive studies and for the detection of physiological states.

Decoding Analysis of Alpha Oscillation Networks on Maintaining Driver Alertness

“…Referring to [ 37 ], the raw EEG data were filtered by wavelet decomposition with 9 levels; after that, wavelet coefficients (7.8–15.6 Hz) at fifth level were used to reconstruct alpha waves. Moreover, the wavelet-based threshold technique in [ 26 ] was used to correct the filtered signals.…”

“…Artificial interactions directly caused by signal mixing neglecting real interactions between neuronal groups at the considered locations can be reduced by a number of binarized connectivity matrices that typically aim to remove linear coupling terms [ 25 ]. Spurious interactions (referred to as ghost interactions) arising from the leakage of signals from a true link of sources to the surrounding links are more difficult to be processed, because of multivariate mixing effects [ 26 , 27 ]. Up to now, steps towards addressing the problem have been taken for suppressing spurious interactions, such as oscillation-based and phase-based estimates [ 28 , 29 ].…”

“…In information theory, entropy represents complexity and uncertainty of information source and embodies information content through the probability distributions that underlie the process of communication [ 32 ]. As a nonlinear estimation of dynamical EEG activity, entropy-based algorithms have been proven to be useful and robust estimators for evaluating regularity or predictability [ 26 , 33 , 34 ]. For example, Shi et al [ 35 ] utilized differential entropy (DE) to extract the EEG features of driver alertness and found it was more accurate and stable comparing with energy spectrum, autoregressive parameters, fractal dimension, and sample entropy.…”

Phase Fluctuation Analysis in Functional Brain Networks of Scaling EEG for Driver Fatigue Detection

“…The adjacent matrix is obtained by computing the magnitude squared coherence between signals from two different channels [20,21]. The magnitude squared coherence C xy is a function of the power spectral densities P xx (f) and P yy (f) of x and y [7,22], and the cross power spectral density P xy (f) of x and y,…”

“…Therefore, by using Equation 5, the adjacent matrix can be computed, as shown in Figure 3. The brain networks under different states have different structural information as the connectivity between different pairs of nodes [22]. In order to give a flavour about the distribution of spatial patterns, Figure 3 provides the weighted functional brain network, in which the spatial topographic distribution obtained a noticeable difference to driver's different states.…”